Surface measures on surfaces of finite codimension in a Banach space. (English. Russian original) Zbl 0716.46041
Math. Notes 47, No. 4, 414-421 (1990); translation from Mat. Zametki 47, No. 4, 147-156 (1990).
Two definitions of surface measures on surfaces of finite codimension are given. An equivalence of this definitions and a theorem on a layer are proved under certain conditions.
Reviewer: R.Norvaisa
MSC:
| 46G12 | Measures and integration on abstract linear spaces |
References:
| [1] | A. V. Uglanov, ?Surface integrals in a Banach space,? Mat. Sb.,110, No. 2, 189-217 (1979). |
| [2] | V. I. Averbukh, O. G. Smolyanov, and S. V. Fomin, ?Generalized functions and differential equations in linear spaces. I. Differentiable measures,? Trudy Mosk. Mat. Obshch.,24, 132-174 (1971). · Zbl 0234.28005 |
| [3] | O. G. Smolyanov, Analysis on Linear Topological Spaces and Its Applications [in Russian], Moscow State Univ. (1979). |
| [4] | S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, N.J. (1964). · Zbl 0129.13102 |
| [5] | J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day, San Francisco (1965). · Zbl 0137.11301 |
| [6] | A. V. Uglanov, ?Surface integrals and differential equations on an infinite-dimensional space,? Dokl. Akad. Nauk SSSR,247, No. 6, 1331-1335 (1979). · Zbl 0429.35070 |
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